Q1. Define conditional probability
Solution
Conditional Probability: If A and B are two events of sample space S associated with a random experiment, then occurrence of A provided B has already occurred is called conditional probability. It is denoted by P(A | B).
Q2. Define posteriori probability
Solution
Posteriori Probability: If E1, E2, ..., En are the partitions of a sample space S, then the probability P(Ei) is called the priori probability of the hypothesis Ei and the conditional probability P(Ei |A) is called a posteriori probability of the hypothesis Ei.
Q3. Define Bernoulli trials.
Solution
Bernoulli Trials: Trials of a random experiment are called Bernoulli trials, if they satisfy the following conditions:
(i) There should be a finite number of trials.
(ii) The trials should be independent.
(iii) Each trial has exactly two outcomes: success or failure.
(iv) The probability of success remains the same in each trial
Q4. Differentiate
sin (2x + 3) w. r. t. x from first principle.
Solution
Not
in current syllabus
Q5. A die is thrown twice and the sum of the numbers appearing is observed to be 9.What is the conditional probability that 4 has appeared atleast once?
Solution
Let A be the event that sum appears to be 9={(3,6),(4,5),(5,4),(6,3)}
B be the event of getting 4 atleast once={(1,4),(2,4),(3,4),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,4),(6,4)}
A
B will be {(4,5),(5,4)}
P(B/A)=
B will be {(4,5),(5,4)}
P(B/A)=
Q6. Define random variable.
Solution
Random Variable: If S is the sample space associated with a random experiment. Then a real valued function which assign to each element of S, a unique real number is called a random variable.
Q7. Consider the Experiment: Throw one die over and over until you get a six; X = the number of throws.What values can X take?
Solution
If you throw a six on the first throw, X = 1. If you first throw one on the second, X = 2, and so on. Thus, the possible values of X are 1, 2, 3, ....
Q8. A bag contains 2 red and 3 black balls . One ball is drawn and put back into the bag.This is done three times and everytime a red ball is drawn, it is counted as a success.Let 'X' denote the number of successes.is 'X' a random variable. Justify your answer
Solution
An experiment is called random experiment if it satisfies the following two conditions: (i) It has more than one possible outcome. (ii) It is not possible to predict the outcome in advance. Here X has two possible outcomes, a success and a failure. It is also not possible to predict the outcome when a ball is drawn, in advance.So X is a random variable.
Q9. Define continuous and discrete random variable.
Solution
(1)Continuous Random Variable: If a random variable X assumes all possible values in a given interval, then it is called continuous random variable.
(2) Discrete Random Variable: If a random variable X assumes only a finite or countable infinite set of values, then it is called discrete random variable.
Q10. What are independent events?
Solution
Independent Events: Two or more events are independent events, such that the probability of occurrence of one event is not affected by occurrence by other.
Comments
Post a Comment